Can I see when my contacts are on line

There is no such feature for what I would hope are obvious privacy issues. You cannot track people online accept with specific apps where you and they use the same app and agree to track each other (e.g. some social media or chat apps that show the online status of your friends who have agreed to allow their status to be shown). But there is no way for you to choose on your own that you want to know someone’s online status with any service.

And things like MS TEAMs let users set their status to available, busy, etc. I know some other apps for online calls or meetings, and some social media apps that allow that. But it is app specific and both users must be using the same app to see each other’s status. And even for any of those like that, it is still up to each user to decide if they want their connection status to be viewable by others. TEAMs has the option to choose “appear away” even when you’re not.

But neither iMessage nor FaceTime have any such setting, nor does anything in any iCloud app have any such setting.

Michael Black wrote:

But neither iMessage nor FaceTime have any such setting, nor does anything in any iCloud app have any such setting.

For which I am very grateful!

That's kind of a vague request. They may be online on one service but not on another. I am "online" here right now, but not "online" in another chat service. Somebody may have their phone turned on but not be "online" anywhere. There aren't too many places with Apple where knowing if somebody is online is really all that useful. Sometimes sending them a Facetime request will get them to then sign into Facetime.

The only place I know of being able to set that specific feature is actually right here on ASC, in your own profile. It's an option and tells you if somebody is logged in right now or when they last logged in. I don't really know how much use it is since this by and large isn't real-time chat anyway.